When the classical theory of problem solving is put into practice, a sequence of operator applications must be found that transforms an initial problem state into a goal state. This is equivalent to finding a path through the graph of possible problem states from an initial node to a goal node. The search is usually conducted by an algorithm or by a human through an iterative process of selecting and applying operators to states found so far. Here, I demonstrate examples of searching in problem spaces via interactive drawing. The demonstrations help to elucidate issues in the design of new problem-solving affordances that may enhance the abilities of human solvers to understand and solve problems. This opens up new ways to conceptualize the process of solving problems, and it suggests new ways to teach a form of computational thinking.